French patent application FR 2,528,122 discloses a pump that enables substance to be dispensed while the pump is either head-up or head-down. The pump comprises a pump body and a moving assembly in the pump body that co-operates therewith to define a pump chamber of variable volume. The pump body includes an opening that enables the substance contained in the receptacle to penetrate into the pump chamber while the pump is in use head-down. The moving assembly includes a lip that enables the opening to be isolated from the pump chamber after the lip has been engaged by a certain amount in the pump body. If the pump is kept head-down over a long period, there possibility exists that the substance might leak out through the opening, particularly if the substance is not very viscous.